Final answer:
The dot product of vectors a = (p, -p, 4p) and b = (2q, q, -q) is calculated as a · b = 2pq - pq - 4pq, which simplifies to a · b = -3pq.
Step-by-step explanation:
The student is asking to find the dot product of two vectors a and b, where a = (p, -p, 4p) and b = (2q, q, -q). The dot product is calculated by multiplying vector components and then adding them. The formula for the dot product of two vectors a = (a1, a2, a3) and b = (b1, b2, b3) is a · b = a1 × b1 + a2 × b2 + a3 × b3.
Therefore, the dot product of vectors is:
a · b = p × 2q + (-p) × q + 4p × (-q)
Which simplifies to:
a · b = 2pq - pq - 4pq
a · b = -3pq
The result of the dot product of vectors a and b is -3pq.